If you have the time, you might locate a local plastics/polycarbonate distributer similar to this company: http://www.usplastic.com/catalog/default.aspx?catid=795&parentcatid=-1 and take your stand there and ask them if they can tell which plastic it is made of and do they have a good adhesive for it.I've recently come into a problem with the support (stand/base/whatever you want to call it) cracking on my Studio Display. It has unfortunately split right through now and no longer supports the monitor. I've tried super gluing it to no avail (It just split again under the weight)
Failing that, I'd try a 30 minute two-part epoxy. Super Glue just doesn't do a very good job of bonding that kind of thing. Good old, I-had-to-mix-it-up-myself epoxy works much better.
But, depending on the plastic used in the base, there may be a solvent type adhesive which will weld the parts back together, such as PVC pipe glue.